Phenotyping in GWAS 1
SUPPLEMENTAL MATERIAL
Power in GWAS:
Lifting the curse of the clinical cut-off
Sophie van der Sluis1
Danielle Posthuma1
Michel G. Nivard2
Matthijs Verhage1
Conor V. Dolan2,3
1
Complex Trait Genetics, Dept. Functional Genomics & Dept. Clinical Genetics, Center for
Neurogenomics and Cognitive Research (CNCR), FALW-VUA, Neuroscience Campus Amsterdam, VU
University medical center (VUmc). Email: s.vander.sluis@vu.nl
2
Biological Psychology, VU University Amsterdam.
3
Department of Psychology, FMG, University of Amsterdam, Roeterstraat 15, 1018 WB
Amsterdam, The Netherlands
Phenotyping in GWAS 2
The simulation
Conditional on the gene-effects, we assumed a normally distributed (N~(0,1)) underlying
latent trait (i.e., the trait of interest that we wish to measure and for which we wish to
identify the genetic background), and we randomly generated latent trait scores for
Nsubj=5000 unrelated subjects. Ten causal variants were then simulated with minor allele
frequency (MAF) of .2 (genotype groups coded 1/2/3 in the phenotype-creating simulation,
with 1 corresponding to the homozygous minor allele genotype), which explained .2 to 2%
of the variance in the latent trait score. Adding the gene-effects to the standard normal
conditional latent trait score resulted in an approximately normally distributed
unconditional latent trait score with a mean of ~1 and a variance of ~1.09.
We then simulated 30 extreme items (Figure S1a) and 30 items that covered the
entire phenotypic range (Figure S1b). The 30 extreme items mainly distinguish between
cases and controls, i.e., between people with and without an extreme phenotype, while the
30 items that cover the entire phenotypic
range also distinguish between subjects
whose phenotype falls well within the
normal range.
Figure S1
S1a: 30 extreme items were simulated,
which distinguish between cases (subjects
scoring on the high end of the phenotypic
distribution) and controls.
S1b. 30 items were simulated that
distinguish between subjects with widely
varying phenotypic scores, ranging from
very low (left on the scale), to average
(middle) to very high (right of the scale, i.e.,
cases) phenotypic scores.
Phenotyping in GWAS 3
The reliability of these items, defined in the context of a latent factor model, ranged
from 0.01 to 0.25 (corresponding to factor loadings ranging from .1 to .5, respectively). In
terms of the internal consistency (Cronbach’s alpha), this resulted in a 30-item instrument
(either consisting of 30 extreme items, or 30 items covering the entire phenotypic range)
with a reliability of .84, which is realistic for depression questionnaires (Beck, Steer &
Garbin, 1988; Radloff, 1991, 1977) and scales that measure behavioural problems like
ADHD (e.g. for Conners’ behavioural rating scales: Sparrow, 2010).
We simulated 3-point scale items (e.g. “0: does not apply”, “1: applies somewhat”,
“2: does certainly apply”), with endorsement rates of the three answer categories
depending on what is called “the difficulty of the item” in the context of Item response
Modelling (IRT). In short, easy items (located at the left of the phenotypic scale, Figure S1b)
are endorsed by almost everybody (i.e., most subjects score 2 on these items), while
difficult items (or extreme items: on the right hand of the phenotypic scale, Figure S1a) are
endorsed by only a small percentage of the general population (i.e., most subjects score 0
on these items). So for the 30 extreme items, 95-98% of the subjects in a normal population
would score 0, 1.5-4 % would score 1, and only .5-1% of subjects in a general population
would score 2 on these items. For the 30 items covering the entire phenotypic range, the
endorsement rates of the three categories varied widely. Figure S2 plots the endorsement
rates for the 30 extreme (Figure S2a) and the 30 items covering the entire phenotypic range
(Figure S2b).
In fact, for every individual, continuous item scores were created first, which were
subsequently categorized. The score on item j for subject i was calculated as
yij = λj*θi + εij ,
where λj denotes the factor loading of item j, θi the latent trait score of subject i, and
εij is the individual-specific residual of the item (i.e., the part of the item score that is not
related to the subject’s latent trait score). The resulting continuous (normally distributed)
item scores were subsequently categorized into 3 scores (0, 1, 2) depending on the
endorsement rates illustrated in Figure S2.
Phenotyping in GWAS 4
Figure S2
Endorsement rates of all the items, which are sorted by “difficulty”, with easy items on the left, and difficult
items on the right hand of the scale. In green the endorsement rate of score 0, in red the endorsement rate of
score 1, and in blue the endorsement rate of score 2 for each of the 30 extreme items (S2a) and each of the 30
items covering the entire phenotypic range (S2b). For these latter items, it can be seen that the easiest items
(left of the scale) are endorsed by almost everyone (score 2 has highest endorsement rate: statement applies to
almost everyone), while the more difficult items (right of the scale) are endorsed by almost no-one (score 0 has
the highest endorsement rate: these statements apply to only a few people).
The categorized item scores of the 30 extreme items and the 30 items covering the entire
phenotypic scale, were subsequently summed to get the individuals’ overall test scores:
sum_skew (based on the 30 extreme items) and sum_tot (based on the 30 items across the
scale).
Using a 2-parameter IRT model, we also calculated the individual subjects’ expected
factor scores, either using their scores on the 30 categorized extreme items, or the 30
categorized items covering the entire phenotypic range.
In addition, the sum score based on the 30 extreme items (sum_skew) was
dichotomized in two ways: we either used a “clinical” cut-off criterion such that the 12%
subjects with the highest sum_skew scores were coded as 1, and the remainder of the
sample as 0, or we coded the highest 50% scoring subjects as 1, and the lowest 50% as 0.
We also categorized the sum_skew score into 3 categories, each covering approximately
Phenotyping in GWAS 5
33% of the sample.
Finally, the sum_skew scores were subjected to a square-root or a normal scores
transformation. Note that these latter two transformations are often recommended before
conducting an analysis like regression (which assumes normally distributed dependent
variables) when the dependent variable of interest (in our case the sum_skew score) is not
normally distributed. The distributions of all 10 discussed phenotypic operationalisations are
illustrated in Figure S3.
Phenotyping in GWAS 6
Figure S3
Based on Nsubj=5000 subjects, the distributions of: A: the simulated
latent trait score θ, B: sum of 30 items covering the entire phenotypic
scale, C: latent factor scores based on the 30 items covering the entire
scale, D: sum of 30 extreme items “sum_skew”, E: square root
transformation of sum_skew, F: Normal scores transformation of
sum_skew, G: latent factor scores based on the 30 extreme items, H:
dichotomized sum_skew (50%-50%), I: dichotomized sum_skew (88%12%), J: categorized sum_skew (33%-33%-33%).
Phenotyping in GWAS 7
All 10 phenotypic operationalizations were subsequently regressed on the 10 causal
variants. In these regression analyses, the homozygous major allele genotype was coded 0
(i.e., carrying 0 minor alleles), the heterozygous genotype was coded 1, and the homozygous
minor allele genotype was coded 2. We also included 1 genetic variant which was not
related to the phenotype so that we could examine the type-I error (false positive) rate.
This entire data simulation + analysis was repeated Nsim=2000 times, and for each
simulated genetic variant we counted the number of times that it was picked up in the
regression given a genome-wide criterion α of 1e-07 (i.e., the number of times out of
Nsim=2000 that the observed p-value in the regression was < 1e-07). The results (in
percentages) are shown in Table S1, and plotted in Figure S4. (Note that Figure S4 is similar
to the published figure in the manuscript, except that a) it also includes the results for other
operationalisations of the phenotype and b) the numbering of the models is different).
In short, the results show that the skewed sum score (2) performs worse than the latent
trait score (1) and the normally distributed sum score (7), and the power decreases
dramatically when the skewed sum score is categorized (3-5), especially when a clinical cutoff criterion is used (3). Clearly, when the trait is polygenic (rather than Mendelian), and
cases and controls differ quantitatively, as stipulated in the common-trait common-variant
hypothesis underlying GWAS, the test statistic associated with the correlation between the
genotype and the case-control phenotype, is generally smaller compared to the test
statistics associated with the other phenotypic measures. This is mainly due to the larger
standard error of the estimate. Consequently, the power to detect the causal locus drops
dramatically.
Phenotyping in GWAS 8
Figure S4
Power plot for simulations using factor loadings ranging from .1-.5, with on the x-axis the effect sizes of the 10
simulated causal genetic variants with MAF=.2 each, and on the y-axis the power to detect these causal variants for
the following phenotypic operationalisations: 1: latent trait, 2: sum_skew, 3: 88-12 dichotomization of sum_skew, 4:
50-50 dichotomization of sum_skew, 5: categorization into 3 equal groups of sum_skew (33-33-33), 6: factor score
based on the 30 extreme, categorized items, 7: sum based on 30 categorized items covering the entire phenotypic
scale, 8: factor score based on the 30 categorized items covering the entire phenotypic scale, 9: square root
transformation of sum_skew, 0: normal score transformation of sum_skew . Results of all 10 scenarios are based on
Nsubj=5000 subjects and Nsim=2000 simulations.
Phenotyping in GWAS 9
Table S1: Power in percentages (for MAF=.2 and factor loadings ranging from .1-.5)
Phenotypic operationalisations
Causal variant effect size (%variance explained)
0.2%
0.4%
0.6%
0.8%
1%
1.2%
1.4%
1.6%
1.8%
2%
Check: 0 %
Latent trait (1)
0.75
10.45
34.20
64.30
85.90
96.10
98.65
99.70
100.00
100.00
5.65
Sum extreme items (2)
0.10
1.15
3.40
11.65
24.80
42.00
56.30
72.20
84.40
90.85
5.50
Dich (88% - 12%) (3)
0.00
0.00
0.05
0.10
0.35
1.05
1.85
3.50
5.90
9.15
5.40
Dich (50%-50%) (4)
0.00
0.15
1.00
3.65
6.20
16.10
25.35
36.00
49.25
59.65
5.25
Categorized (33%/33%33%) (5)
0.00
0.65
2.50
7.20
17.00
31.20
44.90
56.80
71.90
79.85
5.30
Factor score extreme items (6)
0.05
1.15
5.50
17.00
33.55
53.55
68.20
82.40
90.80
95.60
5.55
Sqrt transformation (9)
0.10
1.05
4.15
13.35
27.35
46.05
58.95
74.60
86.30
92.20
5.50
Normal score transformation (0)
0.10
0.95
4.35
14.00
28.20
48.05
61.40
75.85
87.20
93.10
5.65
Sum items covering entire phenotypic range (7)
0.15
2.60
12.55
31.20
53.90
75.50
86.20
93.95
97.95
99.25
4.95
Factor score items covering entire phenotypic
range(8)
0.20
3.30
14.20
35.35
57.60
79.70
89.35
95.40
98.80
99.45
5.35
Note: Power in percentages for simulations using factor loadings ranging from .1-.5: the percentage of Nsim=2000 simulations that picked up the causal variants with
MAF=.2 and with effect size varying from .2 to 2% (i.e., variance explained in the latent trait score). Between brackets the numbers corresponding to Figure S4. The last
column shows the false positive rate given α=.05 (none of the false positive rates deviate significantly from the expected 5%) 1. Nsubj=5000 is all 10 scenarios.
1
Given a nominal α of .05, the percentage of false positive hits is expected to be close to 5%. Note that the standard error of the ML-estimator of the p-value in the
simulations is calculated as sqrt(p*(1 - p)/N), where p denotes the percentage of significant tests observed in the simulations (nominal p-value) given a chosen α, and N the
total number of simulations. The 95% confidence interval for a correct nominal p-value of .05 (given α = .05) and N = 2000 thus corresponds to CI-95 = (p - 1.96 * SE, p +
1.96 * SE), and thus equals .04–.06. This implies that, given α = .05, any observed nominal p-value outside the .04–.06 range should be considered incorrect.
Phenotyping in GWAS 10
To assure generalizability of the simulation results to scenarios in which the MAF of
the causal variants are not .2, we repeated the study with exactly the same simulation
setting except changing minor allele frequencies to MAF=.05 (Figure S5 and Table S2) or to
MAF=.5 (Figure S6 and Table S3). The main results remain the same: dichotomizing a
skewed sum score using a clinical cut-off is very deleterious for the statistical power to
detect causal variants. The difference in power between a skewed sum score and a sum
score based on items covering the entire trait range is less dramatic when MAF is really low
(.05 versus .2 and .5).
In addition, we repeated the simulations with MAF=.2, but changed the settings for
the factor loadings. In the original simulation, the factor loadings ranged between .1 and .5,
which corresponds to inter-item correlations ranging between .01 and .25, which is rather
low but results in a 30-item instrument with a realistic reliability of .84. We added two
simulations: a) factor loadings ranging between .3 and .6 (inter-item correlations between
.09 and .36, and reliability of the 30-item instrument of .91: Table S4 and Figure S7), and b)
factor loadings ranging between .3 and .9 (inter-item correlations between .09 and .81, and
reliability of the 30-item instrument of .98: Table S5 and Figure S8). Again, the main results
remained the same: the power to detect a trait-associated SNP diminishes dramatically if
categorization, and especially a clinical cut-off criterion, is used to dichotomize a skewed but
continuous trait-measure before analysis. In addition, the power of the sum score based on
items covering the entire trait range remains considerably higher compared to the sum
score based on extreme items only.
Phenotyping in GWAS 11
The power of future GWAS studies could thus improve considerably if researchers would
use phenotypic instruments that resolve individual difference in cases as well as controls,
i.e., across the entire trait range. Practically, there are at least two ways in which current
instruments could be adjusted.
1) One could complement the current extreme items with easy items and items of
medium difficulty. This is, however, easier said than done. For example, suppose an
attention deficit /hyperactivity scale like the Child Behavior Check List (CBCL,
Achenbach, 1991) including items like “Often fails to pay close attention or makes
careless mistakes”, “Often does not seem to listen when spoken to directly”, and
“Often has difficulty organizing tasks and activities”. One could add items stating
almost the opposite, e.g., “Pays meticulous attention” and “Listens carefully when
spoken to”, but items of medium difficulty level are difficult to compose.
2) Rather than adding easy/medium items, one could adjust the items’ answer
categories. For instance, answer categories for the attention deficit/hyperactivity
items mentioned above are: “this item describes a particular child not at all / just a
little / quite a bit / very much”. Swanson et al. (2006) suggested to change the
reference of the scale and to rather ask: “compared to other children, does this child
display the following behaviour far below average / below average / slightly below
average / average / slightly above average / above average / far above average”.
These authors developed the SWAN (Strengths and Weaknesses of ADHD symptoms
and Normal behaviour scale), an instrument very much like the CBCL but due to the
different rating scale, overall scores on the SWAN are approximately normally
distributed, while the original CBCL scores are very skewed (see e.g. Polderman et
al., 2007 for an illustration). That is, in asking teachers/parents to compare a child’s
behaviour to the average of other children’s behaviour, and offering not only the
option to display certain behaviour much more often, but also to display it much less
often than average, overall scores on the SWAN are normally distributed in a general
population sample.
For many traits/instruments, changing the answer option and frame of reference,
rather than the actual items, is probably easier to implement in practice. Also, changing
the rating scale is directly applicable to many types of instruments. For instance, the
Phenotyping in GWAS 12
answer option of depression items like “I felt sad”, “I felt lonely”, “I felt my life was a
failure”, and “I felt people disliked me” are usually something like “Rarely / sometimes /
occasionally / often”. Changing the answer options to “compared to other people, did
you feel […] far less often/ less often/ slightly less often/ about as often/ slightly more
often/ more often/ far more often?” is easy to implement. This resulting scale will still
allow distinction between cases and controls, but also distinguishes between controls:
some people do have feelings of loneliness or sadness but only as often as anyone, while
other really hardly ever experience loneliness or sadness.
A drawback of this rescaling, however, could be that participants are not only asked
to evaluate their own behaviour, but to also compare their behaviour to that of others.
This, of course, requires some insight / knowledge about “average behaviour” and what
is considered “average” may differ from person to person. However, answer option like
“rarely” and “occasionally” are also open to subjective evaluation. Self-report
instruments often suffer from this “frame-of-reference” dependency.
Important to note is that simple rescaling will not always result in normally
distributed scores. For instance, schizophrenia symptoms like odd believes, unusual
perceptual experiences, delusions, hallucinations, apathy, and catatonic behaviour are
simply quite extreme and may not be very suited to evaluation on a “gradual” scale.
Whatever strategy one chooses to obtain more normally distributed test scores, the
newly developed instruments of course require careful validation, standardization, and
especially: close comparison to the original instruments for which valuable information
is already available.
Phenotyping in GWAS 13
Figure S5
Power plot for simulations using factor loadings ranging from .1-.5, with on the x-axis the effect sizes of the 10
simulated causal genetic variants with MAF=.05 each, and on the y-axis the power to detect these causal variants for
the following phenotypic operationalisations: 1: latent trait, 2: sum_skew, 3: 88-12 dichotomization of sum_skew, 4:
50-50 dichotomization of sum_skew, 5: categorization into 3 equal groups of sum_skew (33-33-33), 6: factor score
based on the 30 extreme, categorized items, 7: sum based on 30 categorized items covering the entire phenotypic
scale, 8: factor score based on the 30 categorized items covering the entire phenotypic scale, 9: square root
transformation of sum_skew, 0: normal score transformation of sum_skew . Results of all 10 scenarios are based on
Nsubj=5000 subjects and Nsim=2000 simulations.
Phenotyping in GWAS 14
Figure S6
Power plot for simulations using factor loadings ranging from .1-.5, with on the x-axis the effect sizes of the 10
simulated causal genetic variants with MAF=.5 each, and on the y-axis the power to detect these causal variants for
the following phenotypic operationalisations: 1: latent trait, 2: sum_skew, 3: 88-12 dichotomization of sum_skew, 4:
50-50 dichotomization of sum_skew, 5: categorization into 3 equal groups of sum_skew (33-33-33), 6: factor score
based on the 30 extreme, categorized items, 7: sum based on 30 categorized items covering the entire phenotypic
scale, 8: factor score based on the 30 categorized items covering the entire phenotypic scale, 9: square root
transformation of sum_skew, 0: normal score transformation of sum_skew . Results of all 10 scenarios are based on
Nsubj=5000 subjects and Nsim=2000 simulations.
Phenotyping in GWAS 15
Figure S7
Power plot for simulations using factor loadings ranging from .3-.6,with on the x-axis the effect sizes of the 10
simulated causal genetic variants with MAF=.2 each, and on the y-axis the power to detect these causal variants for
the following phenotypic operationalisations: 1: latent trait, 2: sum_skew, 3: 88-12 dichotomization of sum_skew, 4:
50-50 dichotomization of sum_skew, 5: categorization into 3 equal groups of sum_skew (33-33-33), 6: factor score
based on the 30 extreme, categorized items, 7: sum based on 30 categorized items covering the entire phenotypic
scale, 8: factor score based on the 30 categorized items covering the entire phenotypic scale, 9: square root
transformation of sum_skew, 0: normal score transformation of sum_skew . Results of all 10 scenarios are based on
Nsubj=5000 subjects and Nsim=2000 simulations.
Phenotyping in GWAS 16
Figure S8: .3-.9
Power plot for simulations using factor loadings ranging from .3-.9, with on the x-axis the effect sizes of the 10
simulated causal genetic variants with MAF=.2 each, and on the y-axis the power to detect these causal variants for
the following phenotypic operationalisations: 1: latent trait, 2: sum_skew, 3: 88-12 dichotomization of sum_skew, 4:
50-50 dichotomization of sum_skew, 5: categorization into 3 equal groups of sum_skew (33-33-33), 6: factor score
based on the 30 extreme, categorized items, 7: sum based on 30 categorized items covering the entire phenotypic
scale, 8: factor score based on the 30 categorized items covering the entire phenotypic scale, 9: square root
transformation of sum_skew, 0: normal score transformation of sum_skew . Results of all 10 scenarios are based on
Nsubj=5000 subjects and Nsim=2000 simulations.
Phenotyping in GWAS 17
Table S2: Power in percentages (for MAF=.05 and factor loadings ranging from .1-.5)
Phenotypic operationalisations
Causal variant effect size (%variance explained)
0.2%
0.4%
0.6%
0.8%
1%
1.2%
1.4%
1.6%
1.8%
2%
Latent trait (1)
0.80
9.45
36.80
64.25
85.90
94.65
98.85
99.40
99.95
100.00
Sum extreme items (2)
0.00
1.75
9.90
23.80
46.55
65.25
81.90
91.05
96.60
99.00
Dich (88% - 12%) (3)
0.00
0.00
0.00
0.00
0.00
0.05
0.10
0.10
0.30
0.85
Dich (50%-50%) (4)
0.00
0.45
2.15
6.60
14.40
24.35
36.00
52.45
69.50
78.70
Categorized (33%/33%33%) (5)
0.00
0.70
4.50
12.30
26.55
43.15
58.00
71.65
84.85
91.65
Factor score extreme items (6)
0.00
2.50
14.40
31.70
55.20
73.30
88.20
93.95
97.85
99.50
Sqrt transformation (9)
0.10
2.40
13.25
31.05
53.00
71.50
86.55
93.00
97.90
99.30
Normal score transformation (0)
0.05
2.30
12.85
30.60
52.70
70.60
86.65
92.85
97.75
99.35
Sum items covering entire phenotypic range (7)
0.20
2.60
14.45
31.25
53.55
73.70
87.25
93.30
97.75
99.60
Factor score items covering entire phenotypic range(8)
0.30
3.15
15.80
34.75
57.25
77.00
89.90
94.80
98.75
99.70
Note: Power in percentages: the percentage of Nsim=2000 simulations that picked up the causal variants with MAF=.05 and with effect size varying from .2 to 2% (i.e.,
variance explained in the latent trait score). Between brackets the numbers corresponding to Figure S5. Nsubj=5000 is all 10 scenarios.
Phenotyping in GWAS 18
Table S3: Power in percentages (for MAF=.5 and factor loadings ranging from .1-.5)
Phenotypic operationalisations
Causal variant effect size (%variance explained)
0.2%
0.4%
0.6%
0.8%
1%
1.2%
1.4%
1.6%
1.8%
2%
Latent trait (1)
0.90
9.05
34.80
65.60
85.90
95.10
98.75
99.70
100.00
99.95
Sum extreme items (2)
0.00
0.30
1.85
5.05
13.00
22.95
36.15
47.60
60.90
71.60
Dich (88% - 12%) (3)
0.00
0.00
0.00
0.55
0.60
1.55
2.75
3.85
7.20
10.90
Dich (50%-50%) (4)
0.00
0.15
0.50
1.30
3.35
6.55
10.95
16.95
25.35
31.85
Categorized (33%/33%33%) (5)
0.00
0.30
1.10
2.45
6.75
12.20
19.40
28.95
40.55
50.90
Factor score extreme items (6)
0.00
0.50
3.15
7.85
19.10
32.60
46.00
60.75
73.25
83.10
Sqrt transformation (9)
0.00
0.30
1.95
4.60
11.65
21.25
33.25
44.10
58.30
69.60
Normal score transformation (0)
0.00
0.45
2.05
5.20
13.00
24.10
36.75
48.30
62.20
72.60
Sum items covering entire phenotypic range (7)
0.25
2.50
11.80
29.75
52.05
70.70
85.60
91.75
97.10
98.95
Factor score items covering entire phenotypic range(8)
0.25
2.75
13.80
33.35
58.00
75.50
89.00
94.60
98.35
99.35
Note: Power in percentages: the percentage of Nsim=2000 simulations that picked up the causal variants with MAF=.5 and with effect size varying from .2 to 2% (i.e.,
variance explained in the latent trait score). Between brackets the numbers corresponding to Figure S6. Nsubj=5000 is all 10 scenarios.
Phenotyping in GWAS 19
Table S4: Power in percentages (for MAF=.2 and factor loadings ranging from .3-.6)
Phenotypic operationalisations
Causal variant effect size (%variance explained)
0.2%
0.4%
0.6%
0.8%
1%
1.2%
1.4%
1.6%
1.8%
2%
Latent trait (1)
0.45
9.80
35.65
65.50
85.80
95.65
99.30
99.70
100.00
100.00
Sum extreme items (2)
0.05
1.60
7.95
20.20
41.60
61.45
76.15
87.25
94.85
97.55
Dich (88% - 12%) (3)
0.00
0.00
0.30
1.05
1.00
3.75
5.15
10.40
15.65
22.15
Dich (50%-50%) (4)
0.05
0.45
2.65
8.75
16.85
31.15
46.15
61.35
74.90
83.05
Categorized (33%/33%33%) (5)
0.05
1.05
7.50
17.10
34.35
53.25
71.30
81.75
90.20
94.95
Factor score extreme items (6)
0.10
2.95
13.45
30.10
53.95
74.90
86.85
94.60
98.00
99.20
Sqrt transformation (9)
0.10
3.00
12.00
28.75
51.80
71.65
85.05
93.10
97.50
99.20
Normal score transformation (0)
0.10
3.10
12.35
29.05
52.05
72.10
85.60
93.25
97.80
99.25
Sum items covering entire phenotypic range (7)
0.20
5.25
22.40
45.60
69.85
86.55
94.30
98.15
99.70
99.80
Factor score items covering entire phenotypic
range(8)
0.15
4.90
22.55
47.40
71.45
87.35
95.10
98.30
99.55
99.95
Note: Power in percentages: the percentage of Nsim=2000 simulations that picked up the causal variants with MAF=.5 and with effect size varying from .2 to 2% (i.e.,
variance explained in the latent trait score). Between brackets the numbers corresponding to Figure S6. Nsubj=5000 is all 10 scenarios.
Phenotyping in GWAS 20
Table S5: Power in percentages (for MAF=.2 and factor loadings ranging from .3-.9)
Phenotypic operationalisations
Causal variant effect size (%variance explained)
0.2%
0.4%
0.6%
0.8%
1%
1.2%
1.4%
1.6%
1.8%
2%
Latent trait (1)
0.55
10.10
32.50
64.95
85.70
96.70
98.65
99.80
100.00
100.00
Sum extreme items (2)
0.10
2.20
8.70
25.20
49.10
68.45
83.15
92.25
96.45
98.50
Dich (88% - 12%) (3)
0.00
0.05
0.30
0.95
2.30
6.25
11.00
16.60
23.30
31.85
Dich (50%-50%) (4)
0.10
0.65
4.55
14.90
28.90
49.55
64.05
77.50
87.30
93.35
Categorized (33%/33%33%) (5)
0.20
2.35
9.25
25.25
46.80
68.95
81.60
90.90
95.70
98.60
Factor score extreme items (6)
0.30
4.35
17.75
41.95
67.50
86.65
94.60
98.00
99.30
99.85
Sqrt transformation (9)
0.25
4.20
16.40
39.30
63.35
84.10
93.40
97.15
99.15
99.65
Normal score transformation (0)
0.25
4.20
16.40
39.75
64.20
83.85
93.20
97.30
99.20
99.70
Sum items covering entire phenotypic range (7)
0.60
7.80
26.90
56.05
79.95
93.10
97.80
99.60
100.00
99.95
Factor score items covering entire phenotypic
range(8)
0.50
7.80
27.45
56.95
81.15
94.15
97.85
99.60
100.00
99.95
Note: Power in percentages: the percentage of Nsim=2000 simulations that picked up the causal variants with MAF=.5 and with effect size varying from .2 to 2% (i.e.,
variance explained in the latent trait score). Between brackets the numbers corresponding to Figure S6. Nsubj=5000 is all 10 scenarios.
Phenotyping in GWAS 21
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Acknowledgement
Sophie van der Sluis (VENI-451-08-025), Danielle Posthuma (VIDI-016-065-318), and Michel G. Nivard
(912-100-20) are financially supported by the Netherlands Scientific Organization (Nederlandse
Organisatie voor Wetenschappelijk Onderzoek, gebied Maatschappij-en Gedragswetenschappen:
NWO/MaGW). Michel G. Nivard is also supported by the Neuroscience Campus Amsterdam (NCA).
Simulations were carried out on the Genetic Cluster Computer which is financially supported by an
NWO Medium Investment grant (480-05-003), by the VU University, Amsterdam, The Netherlands,
and by the Dutch Brain Foundation.
The R-simulation code is available from the following website:
http://ctglab.nl/people/sophie_van_der_sluis